Adaptation of Sumudu Transform Iterative Method for Solving Fractional Integro-Differential Equations
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Abstract
In this paper, we discussed a new Sumudu transform iterative method and successfully applied on linear and nonlinear fractional integro-differential equations. The obtained results are compatible with those that have been obtained by other methods. The fractional derivative here is described in the Caputo sense. The proposed method is found to be powerful and efficient.
Article Details
How to Cite
[1]
E. Abuteen, “Adaptation of Sumudu Transform Iterative Method for Solving Fractional Integro-Differential Equations ”, AJSE, vol. 21, no. 3, pp. 147 - 151, Dec. 2022.
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References
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[16]F. Kaya, Y. Yılmaz, : Basic Properties of Sumudu Transformation and Its Application to Some Partial differential equations. Journal of Science. 23, 509-514 (2019).
[17] Z. Al-zhour, F. Alrawajeh, N. Al-mutairi, R., Alkhasawneh, : New results on the conformable fractional Sumudu transform: Theories and Applications. International Journal of Analysis and Applications. 17, 1019-1033 (2019).
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[19] Y. A Amer, A. M. S. Mahdy, E. S. M. Youssef, : Solving Systems of Fractional Differential Equations Using Sumudu Transform Method. Asian Research Journal of Mathematics. 7, 1-15 (2017).
[20] S. T. Demiray, H. Bulut, , F. B. M. Belgacem, : Sumudu Transform Method for Analytical Solutions of Fractional Type Ordinary Differential Equations, Mathematical Problems in Engineering. (2015). https//doi.org/10.1155/2014/131690.
[21]R. Jain, D. Singh, : An Integro-Differential Equation of Volterra Type With Sumudu transform, Mathematica Aeterna. 2, 541 – 547 (2012).
[22] Y. A. Amer, A. M. S. Mahdy, H. A. R Namoos, : Application of Sumudu Decomposition Method to Solve Nonlinear System Fredholm and Volterra Integrodifferential Equations, International Journal of Applied Engineering. 13, 9588-9595 (2018).
[23]M. Kumar, V., Daftardar-Gejji, : Exact Solutions of Fractional Partial Differential Equations by Sumudu Transform Iterative Method. Fractional Calculus and Fractional differential Equations. (2019). https//doi.org/10.1007/978-981-13-9227-68
[24] K. Wang, S., Liu, : A new Sumudu transform iterative method for time‑fractional Cauchy reaction–diffusion equation, Springer Plus. 5(1), 865 (2016).
[25] A. A. Hemeda, :New Iterative Method: Application to nth-Order Integro-Differential Equations, International Mathematical Forum. 7, 2317 – 2332(2012).
[26] A. Prakash, M. Kumar, D. Baleanu, : A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform. Applied Mathhmatics and Computations. 334, 30-40 (2018).
[27] H. Anaç, M. Merdan, T. Kesemen, : Solving for the random component time‑fractional partial differential equations with the new Sumudu transform iterative method, SN Applied Sciences. (2020). https//doi.org/10.1007/s42452-020-2625-3.
[28] D. Sh. Mohammed, : Numerical Solution of Fractional Integro-Differential Equations by Least Squares Method and Shifted Chebyshev Polynomial. Mathematical Problems in Engineering. (2014). https://doi.org/10.1155/2014/431965.
[29] Y. Wang, L. Zhu, : Solving nonlinear Volterra integro-differential equations of fractional order by using Euler wavelet method, Advances in Difference Equations. (2017). https//doi.org/10.1186/s13662-017-1085-6.
[2] KS. Miller, B. Ross, : An introduction to the fractional calculus and fractional differential equations. New York: Wiley. (1993).
[3] I. Podlubny, : Fractional differential equations. Academic Press, San Diego. (1999).
[4] A. A. Kilbas, H. M. Srivastava, J.J. Trujillo, : Theory and Applications of Fractional
Differential Equations. North-Holland Mathematics Studies, Elsevier (North-Holland) Science Publishers, Amsterdam, London, and New York. 204, (2006).
[5] K. Diethelm, N. J Ford, : Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications. 265, 229-248(2002).
[6] S.A. Ahmed, T.M. Elzaki, : On the comparative study integro – differential equations using difference numerical methods. Journal of King Abdulaziz University-Science. 32, 84-89(2020).
[7] S. Momani, M. A. Noor, : Numerical methods for fourth-order fractional integro-differential equations. Applied Mathematics and Computation. 182, 754–760 (2006).
[8] P. Das, S. Rana, H. Ramos, : Homotopy perturbations method for solving Caputo type fractional order Volterra-Fredholm integro-differential equations. Computational and Mathematical Methods. (2019). https//doi.org/10.1002/cmm4.1047.
[9] A. Arikoglu, I. Ozkol, : Solution of fractional integro-differential equations by using
fractional differential transform method. Chaos, Solitons and Fractals. 40, 521-529 (2009).
[10] L. Huang, X.F. Li, Y. Zhao, X.Y Duan, : Approximate solution of fractional integro-differential equations by Taylor expansion method, Computers and Mathematics with Applications. 62(3), 1127-1134 (2011). https//doi.org/10.1016/j.camwa.2011.03.037.
[11] E. A Rawashdeh, : Legendre Wavelets Method for Fractional Integro-Differential Equations, Applied Mathematical Sciences. 5(2), 2467 – 2474 (2011).
[12] T.A. Biala, Y.O Afolabi, O.O Asim, : Laplace variational iteration method for integro- differential equations for fractional order. International Journal of Pure and Applied Mathematics. 95, 413-426 (2014).
[13] G. K. Watugala, : Sumudu transform: a new integral transform to solve differential equations and control engineering problems. International Journal of Mathematical Education in Science and Technology. 24, 35–43 (1993).
[14] F. B. M. Belgacem, A. A. Karaballi,: Sumudu transform fundamental properties investigations and applications. Hindawi Publishing Corporation Journal of Applied Mathematics and Stochstic Analysis. (2006). https//doi.org/10.1155/JAMSA/2006/91083.
[15] F. B. M. Belgacem, A. A. Karaballi, S. L. Kalla, : Analytical investigations of the Sumudu transform and applications to integral production equations. Mathematical Problems in Engineering. 3, 103–118 (2003). https//doi.org/10.1155/S1024123X03207018.
[16]F. Kaya, Y. Yılmaz, : Basic Properties of Sumudu Transformation and Its Application to Some Partial differential equations. Journal of Science. 23, 509-514 (2019).
[17] Z. Al-zhour, F. Alrawajeh, N. Al-mutairi, R., Alkhasawneh, : New results on the conformable fractional Sumudu transform: Theories and Applications. International Journal of Analysis and Applications. 17, 1019-1033 (2019).
[18] A. Atangana, A. KJlJçman, : The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat-Like Equations, Abstract and Applied Analysis. (2013). https//doi.org/10.1155/2013/737481.
[19] Y. A Amer, A. M. S. Mahdy, E. S. M. Youssef, : Solving Systems of Fractional Differential Equations Using Sumudu Transform Method. Asian Research Journal of Mathematics. 7, 1-15 (2017).
[20] S. T. Demiray, H. Bulut, , F. B. M. Belgacem, : Sumudu Transform Method for Analytical Solutions of Fractional Type Ordinary Differential Equations, Mathematical Problems in Engineering. (2015). https//doi.org/10.1155/2014/131690.
[21]R. Jain, D. Singh, : An Integro-Differential Equation of Volterra Type With Sumudu transform, Mathematica Aeterna. 2, 541 – 547 (2012).
[22] Y. A. Amer, A. M. S. Mahdy, H. A. R Namoos, : Application of Sumudu Decomposition Method to Solve Nonlinear System Fredholm and Volterra Integrodifferential Equations, International Journal of Applied Engineering. 13, 9588-9595 (2018).
[23]M. Kumar, V., Daftardar-Gejji, : Exact Solutions of Fractional Partial Differential Equations by Sumudu Transform Iterative Method. Fractional Calculus and Fractional differential Equations. (2019). https//doi.org/10.1007/978-981-13-9227-68
[24] K. Wang, S., Liu, : A new Sumudu transform iterative method for time‑fractional Cauchy reaction–diffusion equation, Springer Plus. 5(1), 865 (2016).
[25] A. A. Hemeda, :New Iterative Method: Application to nth-Order Integro-Differential Equations, International Mathematical Forum. 7, 2317 – 2332(2012).
[26] A. Prakash, M. Kumar, D. Baleanu, : A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform. Applied Mathhmatics and Computations. 334, 30-40 (2018).
[27] H. Anaç, M. Merdan, T. Kesemen, : Solving for the random component time‑fractional partial differential equations with the new Sumudu transform iterative method, SN Applied Sciences. (2020). https//doi.org/10.1007/s42452-020-2625-3.
[28] D. Sh. Mohammed, : Numerical Solution of Fractional Integro-Differential Equations by Least Squares Method and Shifted Chebyshev Polynomial. Mathematical Problems in Engineering. (2014). https://doi.org/10.1155/2014/431965.
[29] Y. Wang, L. Zhu, : Solving nonlinear Volterra integro-differential equations of fractional order by using Euler wavelet method, Advances in Difference Equations. (2017). https//doi.org/10.1186/s13662-017-1085-6.